Steve Ray has a list of 35 loaded Questions for "Bible Christians" (quotation marks his)(link to the whole list). This is number 21/35. I'm trying to provide the answers in a common format, for easy reference.
21) Who in the Church had the authority to determine which books belonged in the New Testament canon and to make this decision binding on all Christians? If nobody has this authority, then can I remove or add books to the canon on my own authority?
1) Everyone and no one.
2) Yes and no.
1) As usual, it depends what Steve Ray means. If he means who has the ability to assess whether something is the Word of God, the answer is that all believers have the ability. If Steve Ray means to ask whether that ability is placed infallibly in a single person, the answer is no one.
2) And likewise, yes, anyone can believe or not a particular book, but whether or not someone believes that a book is the Word of God does not change the objective fact of whether that book is the word of God.
3) More to the point, the canon of Scripture is an objective fact. Whether a book is inspired or not is something that we recognize - not something that we "decide" in the sense of exerting an authority over the books themselves. We recognize that by faith, through various instrumentalities - such as history, providence, and the inward moving of the Holy Spirit.